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Unital - Wikipedia, the free encyclopedia Most algebras of functions considered in analysis are not unital, for instance the algebra of square integrable functions (defined on an unbounded domain), and the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space. Given two unital algebras A and B, an algebra homomorphism f : A → B is unital if it maps the identity element of A to the identity element of B. With this assumption, all rings are unital, and all ring homomorphisms are unital, and (associative) algebras are unital iff they are rings. en.wikipedia.org /wiki/Unital   (312 words)

Unital -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-09-18) Given two unital algebras A and B, an algebra (Similarity of form) homomorphism f : A → B is unital if it maps the identity element of A to the identity element of B. The old algebra A is contained in the new one, and in fact A×K is the "most general" unital algebra containing A, in the sense of (Click link for more info and facts about universal construction) universal constructions. If one does, all rings are unital, and all ring homomorphisms are unital, and (associative) algebras are unital (Click link for more info and facts about iff) iff they are rings. www.absoluteastronomy.com /encyclopedia/u/un/unital.htm   (268 words)

Banach algebra   (Site not responding. Last check: 2007-09-18) The algebra of all continuous linear operators on a Banach space E (with functional composition as multiplication and the operator norm as norm) is a unital Banach algebra. The set of invertible elements in any unital Banach algebra is an open set, and the inversion operation on this set is continuous, so that it forms a topological group under multiplication. Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions. nba.servegame.org /en/Banach_algebra.htm   (671 words)

THE STAR HANGER - LETTER NUMBER 6 - EXPANDENCE One cycle of unital translevelence is unifier-unitant translevelence, in which a unifier also functions in the estate of its unitant (or unitants), through alignment with its unitant (or unitants). The other cycle of unital translevelence is unitant-unifier translevelence, in which a unitant (or unitants) also functions at the levelate of its (their) unifier through alignment with its (their) unifier. Within the unity, the unital protoplane is the ground on which we, as unital prototons, walk with sure feet. www.starspring.com /hanger/hanger6.html   (1992 words)

Unital biography .ms   (Site not responding. Last check: 2007-09-18) Some algebras that naturally arise in analysis are not unital, for instance the algebra of functions with compact support on some (non-compact) space. Given two unital algebras A and B, an algebra homomorphism f : A → B is unital if it maps the identity element of A to the identity element of B. If the associative algebra A over the field K is not unital, one can adjoin an identity element as follows: take AxK as underlying K-vector space and define multiplication * by (x,r) * (y,s) = (xy + sx + ry, rs) for x,y in A and r,s in K. unital.biography.ms   (243 words)

THE STAR HANGER - LETTER NUMBER 4 - HETEROLEVELATE UNITIES The vertical hourglass shape comprises the unital walls, and the three horizontal planes--one bounding it at its base and one at its zenith, with a third bisecting its waist--are the subunital planes. In Figure 4-1, the actual unital realities are shown as small beads, lying in the subunital planes, gathered on the periphery of or at the center of the subunital circles. Not restricted to unital function, each is a whole entity that may participate simultaneously in numerous unities. www.starspring.com /hanger/hanger4.html   (2121 words)

PlanetMath: module   (Site not responding. Last check: 2007-09-18) A (unitary or unital) right module is defined analogously, except that the function Cross-references: category, between, equivalence of categories, commutative, operations, scalar, function, unital, unitary, binary operations, identity, ring Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are call unital modules. planetmath.org /encyclopedia/Module.html   (211 words)

[No title] The j-actions are trivial,* * the unit map j is the identity, and the maps fl are the evident identifications. For a unital k-module X with unit 1, define "CX to be the quotient o* *f CX obtained by the identifications (3.6) c x1. Then a C -algebra structure satisfy* *ing j = 0 on a unital k-module A determines and is determined by a "C-algebra struc* *ture on A. The proof is immediate from Proposition 3.4 and the definitions. hopf.math.purdue.edu /Kriz-May/operads_motives.txt   (13330 words)

[No title] It is unital, commutative, and seems to be and H*-algebra by all means, where the inner product is the usual L^2(S^1) inner product. Since the latter is not unital, A isn't unital either. it's not an element of A. Hence A is not unital. www.math.niu.edu /~rusin/known-math/01_incoming/hstar   (846 words)

AMCA: Tensor product of modules over non-unital algebras and Lie-Rinehart algebras by Jan Kubarski   (Site not responding. Last check: 2007-09-18) However, all the technical tools which were used, are appropriate in the case of unital algebras only. If we consider the typical situation where the base ring R is unital, then non-unitality of the R-algebra A means that there is no homomorphism of rings l:R->A such that l(r)a=ra=al(r). The reason is that there is a difference between projective modules in the category of non-unital and unital modules. at.yorku.ca /c/a/j/c/10.htm   (277 words)

The Mizar abstract of POLYNOM5 L%> = <%z0%>; theorem :: POLYNOM5:45 for L be add-associative right_zeroed right_complementable left-distributive unital (non empty doubleLoopStr) for z0,z1,x be Element of L holds eval(<%z0,z1%>,x) = z0+z1*x; theorem :: POLYNOM5:46 for L be add-associative right_zeroed right_complementable left-distributive unital (non empty doubleLoopStr) for z0,z1,x be Element of L holds eval(<%z0,0. L%>,x) = z0; theorem :: POLYNOM5:47 for L be add-associative right_zeroed right_complementable left-distributive unital (non empty doubleLoopStr) for z0,z1,x be Element of L holds eval(<%0. L; end; definition let L be unital (non empty doubleLoopStr); let p be Polynomial of L; attr p is with_roots means :: POLYNOM5:def 7 ex x be Element of L st x is_a_root_of p; end; theorem :: POLYNOM5:55 for L be unital (non empty doubleLoopStr) holds 0_. mizar.uwb.edu.pl /JFM/Vol12/polynom5.abs.html   (1105 words)

[No title] We deone a unital An structure on K as a map ` A(i)+ ^ K(i)-! For n 4, given a (unital or non-unital) An-1 structure on K, the obstruction to extending it to a non-unital An structure lies in Kn-3 (K(n)) ~=Hom3-n((n+1), R), and the obstruction to extending it to a unital An structure (if An-1 is unital) lies in Kn-3 ((K=E)(n)) ~=Hom3-n(~ n, R). The set of non-unital An-1 structures, oxing the An-2 structure, is given by Kn-3 (K(n-1)) ~=Hom3-n(n, R), 4 and the set of unital An-1 structures, oxing the An-2 structure, is given by Kn-3 ((K=E)(n-1)) ~=Hom3-n(~ (n-1), R). hopf.math.purdue.edu /Angeltveit/Ainfinity.txt   (2973 words)

On the Incidence Matrix of the Ree Unital - Hiss (ResearchIndex)   (Site not responding. Last check: 2007-09-18) On the Incidence Matrix of the Ree Unital (1997) Abstract: The dimensions of the codes associated to the Ree unital are computed using methods from modular representation theory. On the incidence matrix of the Ree unital. citeseer.ist.psu.edu /hiss97incidence.html   (397 words)

GAP Manual: 38 Algebras A unital algebra in GAP is an algebra U that is known to contain zero-th powers of elements, and all functions may assume this. The images of unital algebras under operation homomorphisms are either unital or trivial, since the identity of the source acts trivially, so its image under the homomorphism is the identity of the image. An algebra homomorphism of unital algebras is unital if the zero-th power of elements in the source is mapped to the zero-th power of elements in the range. schmidt.nuigalway.ie /gap/CHAP038.htm   (2936 words)

Unitals   (Site not responding. Last check: 2007-09-18) A unital in the classical projective plane PG_2(q^2) is a set of q^3 + 1 points such that every line meeting two of these points meets exactly q + 1 of them. The set of intersections of the unital U with the tangents to U which pass through the point p. The following code computes the Hermitian unital given by the equation x^(q + 1) + y^(q + 1) + z^(q + 1) = 0 in PG_2(q^2) for q = 3. www.umich.edu /~gpcc/scs/magma/text1230.htm   (293 words)

Coalgebra   (Site not responding. Last check: 2007-09-18) In mathematics, coalgebras are structures that are in a certain sense dual to the unital associative algebras. One formulates the axioms of unital associative algebras in terms of commutative diagrams, and then turns all arrows around to get the axioms of coalgebras. In a certain sense then, coalgebras are generalizations of (duals of) finite-dimensional unital associative algebras. www.worldhistory.com /wiki/C/Coalgebra.htm   (956 words)

Web Traders Trade Import Export South Africa   (Site not responding. Last check: 2007-09-18) UniTal Films International has offices in central London, Johannesburg and Perth. UniTal ensures that you get the best screen value possible for your budget - wherever you want to shoot. As a leading South African production company, UniTal has been making feature films and TV drama for over 20 years. www.webtraders.co.za /directory/F/film.htm   (118 words)

PlanetMath: module   (Site not responding. Last check: 2007-09-18) In this case we may say that the module is unital. module action, left module action, right module action, unital module Cross-references: right notation, sides, inverses, identity element, operator, terms, additive, structure, map, identity, unital, function, left function notation, composition, endomorphisms, ring homomorphism, abelian group, ring planetmath.org /encyclopedia/UnitalModule.html   (172 words)

[No title]   (Site not responding. Last check: 2007-09-18) \item{\bf 4.} Let $R$ be a finite commutative unital ring in which 0 is the only nilpotent element. \ g\in G, t\in T\}$, where $G_{gt}$ is the stabilizer of $gt$ in $G$, is normal in G The \ut{radical}, $\Rad(R)$, of a unital ring $R$ is the intersection of the maximal ideals of $R$. If $\phi:R\longrightarrow S$ is a surjective unital ring homomorphism, then $\phi(\Rad(R)) \subseteq \Rad(S)$. darkwing.uoregon.edu /~anderson/math647/final.html   (134 words)

Atlas: Intrinsic centrality and associated classifying properties by Dominique Bourn The notion of unital category is a special case of pointed category, which allows to characterize Mal'cev categories via the fibration \pi of pointed objects. The major examples of unital categories are the categories Mon, CoM, Gp, Ab, Rg of respectively monoids, commutative monoids, groups, abelian groups, rings, and the categories Mag(E), Mon(E), CoM(E), Gp(E), Ab(E), Rg(E) of respectively internal unitary magmas, monoids, commutative monoids, groups, abelian groups, rings in a left exact category E. The aim of this work is to show that, inside any unital category C, there is an additive core which has a powerful classifying potential. atlas-conferences.com /cgi-bin/abstract/cajf-46   (577 words)

Townhall.com :: Columns :: Drawing the line - again and again and again by Paul Greenberg   (Site not responding. Last check: 2007-09-18) Yet they scoff at our fears and dream of creating the perfect race of men - (ital) sans (unital) sickness, (ital)sans (unital) deformity, (ital) sans (unital) suffering and (ital) sans (unital) pity. There is something unthinking, something almost frivolous, in the unexamined assumption that Science should do something because it (ital) can (unital) be done. Even old Socrates, the prime representative of reason in the Western tradition, claimed to have had a guardian spirit. www.townhall.com /columnists/paulgreenberg/pg20010806.shtml   (1103 words)

Unital Films International Home: Feature Films, TV & Documentaries We are based in Johannesburg with offices in Durban and Cape Town. We formed a British company, UniTal UK Ltd., in 1999 and opened our London office. Recently several additions and changes have been made to the original team and UniTal Films has emerged on the international scene as a strong player offering both financial and creative assistance to global producers. www.unitalfilms.com   (175 words)

About Unital Films International United Talents is based in Johannesburg, with offices in Durban and Cape Town. UniTal Films assists in structuring finance for projects suited UniTal Films International ensures delivery of great screen values for foreign and local film production. www.unitalfilms.com /aboutus   (359 words)

Townhall.com :: Columns :: Why I love Mississippi by Paul Greenberg   (Site not responding. Last check: 2007-09-18) Not since I mixed up my Fatses, and confused Waller with Domino, have I been inundated by so many letters and e-mails from Mississippi, that great storehouse of Southern language and literature. For the record, it was Fats (ital) Waller (unital) who contributed what I still consider one of the great summations of the human condition, to wit: One never knows, do one? Granted, it's not exactly a scientific poll, and even if it were, literary greatness is scarcely subject to majority vote. www.townhall.com /columnists/paulgreenberg/pg20010823.shtml   (1019 words)

Proceedings of the American Mathematical Society Abstract: Characterisations and containment results are given for linear subspaces of a unital C*-algebra that are invariant under conjugation by sets of unitary elements of the algebra. The (unitarily-invariant) linear span of the projections in a simple, unital C*-algebra having non-scalar projections is shown to contain all additive commutators of the algebra and, in certain cases, to be equal to the algebra. B.E. Blackadar, A simple unital projectionless C*-algebra, J. Operator Theory 5 (1981), 63-71. www.ams.org /proc/1998-126-12/S0002-9939-98-04934-X/home.html   (293 words)

No Title   (Site not responding. Last check: 2007-09-18) In 1947, Kaplansky proved the classical result that if C(X) and C(Y) are isomorphic as lattices for two compact Hausdorff spaces X and Y, then X and Y are homeomorphic. In 1968, by extending the arguments used by Kaplansky, Subramanian proved the generalization for f-rings: if two unital commutative Moreover, it is shown that the structure space of a unital www.math.utep.edu /events/coll-abstracts/110300   (224 words)

K-theory for C*-algebras   (Site not responding. Last check: 2007-09-18) However, I strongly recommend that you do the exercises on a regular basis during the semester! -group of a unital ring (RLL, Chapter 1, Section 3.1, and Exercise 3.10). -group of a unital C*-algebra: Murray-von Neumann equivalence and unitary equivalence of projections (RLL, parts of Sections 3.1-3.2 and 2.2-2.3). www.math.ku.dk /~laustsen/E04/ktheory.html   (389 words)

Atlas: Linear Preserver Problems on Matrix Algebras over Unital Commutative Rings by Wen-Fong Ke   (Site not responding. Last check: 2007-09-18) We use the theory of functional identities to describe maps preserving square-zero matrices over unital commutative rings. Then we apply the result to describe maps preserving idempotents and local automorphisms. The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canq-80. atlas-conferences.com /cgi-bin/abstract/canq-80   (100 words)

KK-theory of the full free product of unital (ResearchIndex)   (Site not responding. Last check: 2007-09-18) KK-theory of the full free product of unital Abstract: We establish in this paper the existence of a long exact sequence in KK-theory for the full free product of unital C -algebras having the Knuclearity property. It was first conjectured by Cuntz in 1982 and only proved so far for C -algebras having a one dimensional representation or for reduced (discrete) group C -algebras. citeseer.ist.psu.edu /520962.html   (285 words)

Operator algebra seminar During the last decade there has been considerable progress in the theory of classification of simple unital C Our main result is that the Elliott invariant is a complete invariant for the class of simple unital inductive limits of finite direct sums of building blocks, provided that either K -algebras is that it contains simple unital projectionless C www.math.ku.dk /cal/events/484.htm   (158 words)

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